Let h(x) = tan(3x + 8). Then h'(5) is and h''(5) is

Q: Find the derivative of the function f(x) = = sin(x) - 1 cos(2x) + 1 4

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Q: Find the derivative, dy/dx: y = x² In x3 ý =- 2 1-4 ln x x³ In? x 3. ý = -2 In x – 2x | y = --(- 3…

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Q: [In(x²)-ex cos(x-1).tan(Tx) 20. lim 2x2-x sin2(1-x) X-1

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Q: Evaluate the derivative of y = cos '2x - In 1-4x, where x = 0.125 -12> 2

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Q: Find derivative of the following functions 1. y= sin^-1 2x^2 2. y= tan^-1 2x^2/5

A: Given 1. y=sin-1(2x2)2. y=tan-1(2x25)

Q: find f'(x) if f(x) = tanh(ln x) +sin2(2x)

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Q: Find the Equation of tangent line of the function f(x) = 1 + csc(x) – /cos(x) 2n 4+V3 23 At the…

A: Consider the provided function, fx=1+cscx-cosx and the given point 2π3,4+323. Find the equation of…

Q: |2tan x In (cos x) dx=

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Q: 2) Find the derivative of f(x) = tan(1+ cos 3 x) %3D

A: As the function involved function in a function we can apply chain rule and find the derivative of…

Q: 2. Find the derivatives of Y with respect to x if; x=arc sin ex.

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Q: Find the derivative of 2 cos x 1. f(x) x+1

A: As we know that: The Power rule: ddxxn=nxn-1 The Quotient rule: fg'=f'·g-g'·fg2 Given: fx=2cosxx+1

Q: 1. Find the first derivative " if y = x sin 27x . dx

A: Given:  y=x sin 2πxTo determine the firstderivative.

Q: 2tan x In (cos x) dx=

A: here we have to integrate the given integral.

Q: Which is the derivative of y= sin (x2-2x + 1)? (2х -2) (2x-2)Cos(x²-2x + 1)

A: We have to find derivative

Q: Find the first derivative for y = 5 cos x

A: Given,          y=5cosx

Q: find integral tan 3 x dx

A: To find the integral of tan2x first split tan into two part and the using property of sec and tan…

Q: Consider the function f(x) whose second derivative is f′′(x) = 18x + 3 cos x. If f(0) = 4 and f′(0)…

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Q: derive ^x dx cos"x Sinx + n-1 Cash Cos"-2x dx n-2, X. Jos"x dx in

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Q: Find the tangent line to the function f(x) = 2x cos4(x) at the point (0,1)

A: We have given function fx=2xcos4x and point 0,1. We have to find tangent line to the function at the…

Q: Find the most general anti-derivative of f(x) = 9Vx +1+ cos x.

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Q: Find the Equation of tangent line of the function f(x) = 1+ csc(x) – cos(x) 2n 4+v3 3' 23 At the…

A: Answer

Q: Find the derivative of y with respect to x. -1 y = tan (In(2x))

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Q: Compute the derivative f'(x)given sin x 1 dt 1- 12 f(x) = cos x

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Q: Find the derivative of y with respect to x. y = In (tan -1 (9x5))

A: Given : y=lntan-19x5

Q: Find the differential for y = tan 2x2

A: Find the differential equation for given equation We need to take derivative for tan using the…

Q: Find the derivative: f(x) = cos 1 + e8x 1- e6x – ebz f'(x) =

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Q: Find the derivative of h(x) = (1+ cos x)*

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Q: 1) Find the derivative of f(x) 1+sin 2 x %3D 2 cos x

A: we are given the function is  f(x)=1+sin2x2cos3x

Q: Use forward-difference formula to evaluate the first derivative of y = tan(x) at x = 4 using a value…

A: Given function is y=tanx. We have to find the first derivative of y=tanx at x=π4 using a value of…

Q: 5. Find the derivative of the following. 3x-5 а. у3 b. y = In (sin(3x-5)) c. y= e2x arc tan (2x + 3)…

A: Explanation of the answer is as follows

Q: Find if dy dx y = (cos x) * O (cos x) * (-sin x) O (sin x) * (In cos x - x tan x) O (sin x)* (In cos…

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Q: Find the derivatives of the functions h(x) = x tan (2√x) + 7

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Q: Find the first derivative of * In (sec y + tan y) - x - sinx = 2 O tany (cos.x + 1) O cos y (cos x +…

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Q: 3. Find the derivative D(x *arctan(x)) And the integral 6x dx 9+x

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Q: Find the derivative of both a and b a. x csc-1(1/x) b.(esin2x)/[In(cos2x)]2

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Q: Use your knowledge on Higher-order derivative and Chain Rule to show that z" + 4z' + 8z = 0 if z =…

A: Show that, z''+4z'+8z=0 if z=e-2xsin2x+cos2x Formulas used:…

Q: Use the chain rule to find the derivative of: cos(7 + 8x)

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Q: What are the first and second derivatives of f(x) = cos 2x ?

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Q: find the derivative of f(x)=(x^4+3x^2+8)cos

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Q: Find sixth order derivative of the function f(x) = (x – 5)7.cos(5x) by using %3D Leibnitz theorem.

A: If y=uv where, u and v are functions of x then un and vn denote the nth derivative of u and v with…

Q: 16. What is the derivative of the function: * y = sin(6x² - 1) y = 12x cos(6x² - 1) y' = x cos(6x² -…

A: Solving the problem by finding the value of the derivative.

Q: In (sinh x ), + tanh x j + 1-x k )dx 1- sinx

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Q: Compute the derivative d tan x dx \cos x – 4)

A: To compute :

Q: Differentiate implicitly for the equation for x^2y+x^3-cos(x)=3y^2

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Q: Compute the derivative d tan x dx \cos x – 4

A: Given: Formula Used:

Q: Find the derivative of y with respect to x. y= In (tan (4x*))

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Q: Can you help me step by step?

A: Given function,

Q: How are the derivatives of sin-1 x and cos-1 x related?

A: Given functions are sin-1x and cos-1x

Q: What is the derivative of the function h(x) = ((4x^2-4)/(cos(x)))^8

A: We have to find the derivative of ((4x^2-4)/(cos(x)))^8 = 4^8(x^2-1) sec^8(x)= 65536(x^2-1)sec^8(x)